Among those compounds, \(\mathrm {Mn_3Ge}\)  has been found to exhibit a large intrinsic anomalous Hall effect even at room temperature and this effect is strongly anisotropic and can be switched with a small applied magnetic field [1]}, [2]}.
These interesting transport properties are attributed to the peculiar magnetic patterns of the Mn spins.
The hexagonal Mn\(_3\) Ge is a noncollinear antiferromagnetic crystal with antichiral spin structure in the basal plane below the Néel temperature \(T_\mathrm {N}\)  ranging from \(365 \, \mathrm {K}\)  to \(400\, \mathrm {K}\)  [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [2]}.
The resulting electron bands can support Weyl points that act as effective monopoles generating large Berry curvatures at the Fermi surface [10]}, [11]}, [12]}.
Nevertheless, the magnetic anisotropies of the Mn\(_3\) X family have long been investigated and debated. The torque measurements in Mn\(_3\) Sn indicate a six-fold symmetry and another two-fold symmetry of the magnetic anisotropy [13]}. While a near cubic symmetry of the anisotropy is found in noncollinear antiferromagnet \(\mathrm {L1_2}\) -ordered Mn\(_3\) Ir, which is never found in ferromagnets [14]}, [15]}, [16]}. In addition, an extremely strong second-order anisotropy appears in Mn\(_3\) Ir due to its frustrated triangular magnetic ground state [17]}. For Mn\(_3\) Ge it was argued that no in-plane anisotropy energy exists up to four-fold terms [5]}, [4]}, [1]},
because the second- and the fourth-order anisotropy energies from each Mn site cancel out and cannot induce significant energy landscapes [21]}.
However, a weak in-plane ferromagnetic moment with nearly isotropic susceptibility is detected in Mn\(_3\) Ge [6]}, [5]}. The origin of this small ferromagnetism is not yet clarified and can be determined by either spin-orbit coupling effects [24]}, [10]}, [26]} or the local spin anisotropy [21]}, [28]}, [29]}. Besides, the magnetic anisotropy for fields applied along different crystallographic directions have not been thoroughly evaluated, despite of the availability of neutron diffraction studies [30]}, [29]}.
